cp's OEIS Frontend

A360497 Maximal sequence of primes whose digits are primes and whose digit sum is also a term.

%I A360497 #34 Mar 05 2023 19:49:45
%S A360497 2,3,5,7,23,223,2777,7727,27527,33377,33773,35537,35573,35753,37337,
%T A360497 52727,55337,55373,55733,73553,75227,75353,75533,222557,222773,223277,
%U A360497 225257,225527,233357,235337,235553,253553,253733,277223,322727,323537,332573,335273
%N A360497 Maximal sequence of primes whose digits are primes and whose digit sum is also a term.
%C A360497 The sequence is maximal in the sense that a nonempty set of primes cannot be added consistently.
%e A360497 2 is a term because it is a prime with prime digits only and its digit sum 2 is also a term.
%e A360497 227 is not a term because the digit sum is 11 which is not a term because it has nonprime digits.
%e A360497 27527 is a term: it is a prime, each digit (2,5,7) is also a prime, and the sum of the digits (2+7+5+2+7 = 23) is also in the sequence.
%p A360497 R:= {2,3,5,7}: count:= 4:
%p A360497 S:= [2,3,5,7];
%p A360497 for d from 2 to 11 do
%p A360497   S:= map(t -> (10*t+2,10*t+3,10*t+5,10*t+7), S);
%p A360497   for x in S do
%p A360497     if member(convert(convert(x,base,10),`+`),R) and isprime(x) then
%p A360497        R:= R union {x}; count:= count+1;
%p A360497     fi
%p A360497   od;
%p A360497 od:
%p A360497 sort(convert(R,list)); # _Robert Israel_, Mar 02 2023
%o A360497 (Python)
%o A360497 from sympy import isprime
%o A360497 seq = [2, 3, 5, 7]
%o A360497 for i in range(9, 10**6, 2):
%o A360497     s = str(i)
%o A360497     if set(s) <= set("2357") and sum(map(int, s)) in seq and isprime(i):
%o A360497         seq.append(i)
%o A360497 print(seq)
%Y A360497 A subsequence of A062088.
%Y A360497 Cf. A000040, A007953.
%K A360497 nonn,base
%O A360497 1,1
%A A360497 _Hongwei Jin_, Feb 09 2023